Gaming devices such as slot, poker, blackjack and keno machines having primary games and secondary or bonus games or schemes are well known. One well known bonus game provides a player with a series of different award offers consisting of credits or dollars. The player may accept or reject any individual award offer in the series, however, the player must accept the final award offer if no previous award offer is accepted. If the player accepts an award offer, the player keeps the award and the bonus game terminates. If the player rejects the award offer, the gaming device provides a new award offer for player acceptance. The bonus game continues to provide new award offers until an award offer is accepted or the award offer is the final award offer.
Several implementations of this type of bonus scheme have been employed in gaming machines of various types. While this type of gaming device has achieved significant popularity in the gaming industry, players may lose interest in the game after playing the game repeatedly. Accordingly, there is a need for new gaming devices having improved award offer bonus schemes.